week3-1 - Assignment Assignment#2 Forsubmission 5.8 5.30...

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ssignment #2 Assignment #2 For submission .8 .30 .40 5.8 5.30 5.40 For practice 5.20 5.29 5.35 Td J 2 12 Due Tuesday, January 2 th at 12 noon
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b exemptions Lab exemptions Exempt 110228331 60150531 260150531 260164335 60193315 260193315 260211586 260229378 260230341 260233669 260254007
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rsion Torsion Twisting of an object due to an applied torque Torque moment that tends to twist a member (often a A moment that tends to twist a member (often a circular shaft) about its longitudinal axis Simplest case Circular (hollow or solid) shaft
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rsion Torsion Torque A moment that tends to twist a member (often a rcular shaft) about its longitudinal axis circular shaft) about its longitudinal axis
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ircular Shafts Circular Shafts After twisting Plane sections remain planar Radial line on cross section remains straight
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uare Sections Square Sections After twisting Plane sections do not remain planar More complex analysis
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rsional ear Strain Torsional Shear Strain After applying torque (T) Longitudinal lines twist into helixes Free end of shaft rotates through an angle φ Shaft length remains constant Angle of twist varies linearly with length
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rsional ear Strain Torsional Shear Strain General case where 0 < ρ < R Both faces rotate…. C to C’ and D to D’ ngular difference between Angular difference between the rotations of the two faces is equal to φ q
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rsional ear Strain Torsional Shear Strain φ ρΔ = D D D D Δ = = ρ γ tan x x Δ Δ γ= tan For small angles
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rsional ear Strain Torsional Shear Strain as the dx d φ ρ γ= So, as the segment length es to zero goes to zero dx d is angle of twist per unit length 0 at ρ = 0 max γ at ρ = R
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rsional ear Strain Torsional Shear Strain dx d R φ γ = max dx d ρ γ= combine with ax Shear strain at any R max = radial coordinate
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rsional ear Stress Torsional Shear Stress ε σ E = Recall, for axial loading γ τ G = Similarly, for torsional loading Stress is proportional to strain G= Shear modulus or modulus of rigidity pplies up to proportional limit ( r Applies up to proportional limit (ie for elastic deformation)
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rsional ear Stress Torsional Shear Stress γ max = r rsional rain ρ R For torsional strain τ R max = For torsional stress
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This note was uploaded on 12/01/2009 for the course CIVE 207 taught by Professor Shao during the Winter '09 term at McGill.

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week3-1 - Assignment Assignment#2 Forsubmission 5.8 5.30...

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